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New fifth and seventh order mock theta function identitiesJul 10 2019We give simple proofs of Hecke-Rogers indefinite binary theta series identities for the two Ramanujan fifth order mock theta functions $\chi_0(q)$ and $\chi_1(q)$ and all three of Ramanujan's seventh order mock theta functions. We find that the coefficients ... More

Transformation properties for Dyson's rank functionJan 21 2016Sep 08 2016At the 1987 Ramanujan Centenary meeting Dyson asked for a coherent group-theoretical structure for Ramanujan's mock theta functions analogous to Hecke's theory of modular forms. Many of Ramanujan's mock theta functions can be written in terms of $R(\zeta,q)$, ... More

Congruences and relations for r-Fishburn numbersJun 21 2014Recently Andrews and Sellers proved some amazing congruences for the Fishburn numbers. We extend their results to a more general sequence of numbers. As a result we prove a new congruence mod 23 for the Fishburn numbers and prove their conjectured mod ... More

Rank-Crank type PDEs and generalized Lambert series identitiesJan 08 2012We show how Rank-Crank type PDEs for higher order Appell functions due to Zwegers may be obtained from a generalized Lambert series identity due to the first author. Special cases are the Rank-Crank PDE due to Atkin and the third author and a PDE for ... More

A q-product tutorial for a q-series MAPLE packageDec 16 1998This is a tutorial for using a new q-series Maple package. The package includes facilities for conversion between q-series and q-products and finding algebraic relations between q-series. Andrews found an algorithm for converting a q-series into a product. ... More

Universal mock theta functions and two-variable Hecke-Rogers identitiesFeb 08 2014We obtain two-variable Hecke-Rogers identities for three universal mock theta functions. This implies that many of Ramanujan's mock theta functions, including all the third order functions, have a Hecke-Rogers-type double sum representation. We find new ... More

Automatic Proof of Theta-Function IdentitiesJul 20 2018This is a tutorial for using two new MAPLE packages, thetaids and ramarobinsids. The thetaids package is designed for proving generalized eta-product identities using the valence formula for modular functions. We show how this package can be used to find ... More

The spt-crank for overpartitionsNov 14 2013Dec 11 2014Bringmann, Lovejoy, and Osburn showed that the generating functions of the spt-overpartition functions spt(n), spt1(n), spt2(n), and M2spt(n) are quasimock theta functions, and satisfy a number of simple Ramanujan-like congruences. Andrews, Garvan, and ... More

Exotic Bailey-Slater SPT-Functions II: Hecke-Rogers-Type Double Sums and Bailey Pairs From Groups A, C, EJan 27 2015Jul 06 2016We investigate spt-crank-type functions arising from Bailey pairs. We recall four spt-type functions corresponding to the Bailey pairs $A1$, $A3$, $A5$, and $A7$ of Slater and given four new spt-type functions corresponding to Bailey pairs $C1$, $C5$, ... More

On the Andrews-Stanley Refinement of Ramanujan's Partition Congruence Modulo 5Jan 03 2004In a recent study of sign-balanced, labelled posets Stanley [13], introduced a new integral partition statistic srank(pi) = O(pi) - O(pi'), where O(pi) denotes the number of odd parts of the partition pi and pi' the conjugate of pi. In [1] Andrews proved ... More

The GBG-Rank and t-Cores I. Counting and 4-CoresJul 30 2008Aug 14 2008Let r_j(\pi,s) denote the number of cells, colored j, in the s-residue diagram of partition \pi. The GBG-rank of \pi mod s is defined as r_0+r_1*w_s+r_2*w_s^2+...+r_(s-1)*w_s^(s-1), where w_s=exp(2*\Pi*I/s). We will prove that for (s,t)=1, v(s,t) <= binomial(s+t,s)/(s+t), ... More

Some Observations on Dyson's New Symmetries of PartitionsMar 12 2002Apr 23 2002We utilize Dyson's concept of the adjoint of a partition to derive an infinite family of new polynomial analogues of Euler's Pentagonal Number Theorem. We streamline Dyson's bijection relating partitions with crank <= k and those with k in the Rank-Set ... More

Combinatorial interpretations of Ramanujan's tau functionJun 26 2016We use a q-series identity by Ramanujan to give a combinatorial interpretation of Ramanujan's tau function which involves t-cores and a new class of partitions which we call (m,k)-capsids. The same method can be applied in conjunction with other related ... More

On the Andrews-Stanley Refinement of Ramanujan's Partition Congruence Modulo 5 and GeneralizationsFeb 26 2004In a recent study of sign-balanced, labelled posets Stanley, introduced a new integral partition statistic srank(pi) = O(pi) - O(pi'), where O(pi) denotes the number of odd parts of the partition pi and pi' is the conjugate of pi. Andrews proved the following ... More

Dissecting the Stanley Partition FunctionSep 24 2004Mar 02 2005Let p(n) denote the number of unrestricted partitions of n. For i=0, 2, let p[i](n) denote the number of partitions pi of n such that O(pi) - O(pi') = i mod 4. Here O(pi) denotes the number of odd parts of the partition pi and pi' is the conjugate of ... More

Hecke-type congruences for Andrews' spt-function modulo 16 and 32Jun 06 2013Aug 22 2013Inspired by recent congruences by Andersen with varying powers of 2 in the modulus for partition related functions, we extend the modulo 32760 congruences of the first author for the function spt(n). We show that a normalized form of the generating function ... More

The BG-rank of a partition and its applicationsFeb 16 2006Apr 28 2007Let \pi be a partition. In [2] we defined BG-rank(\pi) as an alternating sum of parities of parts. This statistic was employed to generalize and refine the famous Ramanujan modulo 5 partition congruence. Let p_j(n)(a_{t,j}(n)) denote a number of partitions ... More

Shifted and Shiftless Partition Identities IIMay 12 2006Let S and T be sets of positive integers and let a be a fixed positive integer. An a-shifted partition identity has the form p(S,n)=p(T,n-a), for all n greater or equal to a. Here p(S,n) is the number partitions of n whose parts are elements of S. For ... More

K. Saito's Conjecture for Nonnegative Eta ProductsJul 25 2006We prove that the Fourier coefficients of a certain general eta product considered by K. Saito are nonnegative. The proof is elementary and depends on a multidimensional theta function identity. The z = 1 case is an identity for the generating function ... More

K. Saito's Conjecture for Nonnegative Eta Products and Analogous Results for Other Infinite ProductsFeb 01 2007We prove that the Fourier coefficients of a certain general eta product considered by K. Saito are nonnegative. The proof is elementary and depends on a multidimensional theta function identity. The z=1 case is an identity for the generating function ... More

Congruences for Generalized Frobenius Partitions with an Arbitrarily Large Number of ColorsMay 26 2013In his 1984 AMS Memoir, George Andrews defined the family of $k$--colored generalized Frobenius partition functions. These are denoted by $c\phi_k(n)$ where $k\geq 1$ is the number of colors in question. In that Memoir, Andrews proved (among many other ... More

Congruences for Andrews' spt-function modulo powers of 5, 7 and 13Nov 09 2010Congruences are found modulo powers of 5, 7 and 13 for Andrews' smallest parts partition function spt(n). These congruences are reminiscent of Ramanujan's partition congruences modulo powers of 5, 7 and 11. Recently, Ono proved explicit Ramanujan-type ... More

Biranks for Partitions into 2 ColorsSep 26 2009In 2003, Hammond and Lewis defined a statistic on partitions into 2 colors which combinatorially explains certain well known partition congruences mod 5. We give two analogs of Hammond and Lewis's birank statistic. One analog is in terms of Dyson's rank ... More

Higher Order SPT-FunctionsAug 06 2010Oct 30 2010Andrews' spt-function can be written as the difference between the second symmetrized crank and rank moment functions. Using the machinery of Bailey pairs a combinatorial interpretation is given for the difference between higher order symmetrized crank ... More

Congruences for Andrews' spt-function modulo 32760 and extension of Atkin's Hecke-type partition congruencesNov 09 2010New congruences are found for Andrews' smallest parts partition function spt(n). The generating function for spt(n) is related to the holomorphic part alpha(24z) of a certain weak Maass form M(z) of weight 3/2. We show that a normalized form of the generating ... More

Congruences for Andrews' Smallest Parts Partition Function and New Congruences for Dyson's RankOct 31 2007Jun 11 2008Let spt(n) denote the total number of appearances of smallest parts in the partitions of n. Recently, Andrews showed how spt(n) is related to the second rank moment, and proved some surprising Ramanujan-type congruences mod 5, 7 and 13. We prove a generalization ... More

Experimental observation of transient velocity-selective coherent population trapping in one dimensionJan 27 2005We report the observation of transient velocity-selective coherent population trapping (VSCPT) in a beam of metastable neon atoms. The atomic momentum distribution resulting from the interaction with counterpropagating sigma_+ and sigma_- radiation which ... More

Theory Vision, LHCP 2016Sep 22 2016I give my perspective on promising directions for high energy physics in coming years.

Hilbert C*-modules over monotone complete C*-algebrasAug 31 1994Jul 27 2010The aim of the present paper is to describe self-duality and C*- reflexivity of Hilbert {\bf A}-modules $\cal M$ over monotone complete C*-algebras {\bf A} by the completeness of the unit ball of $\cal M$ with respect to two types of convergence being ... More

Rotation Numbers and Instability SetsMar 24 2003Translation and rotation numbers have played an interesting and important role in the qualitative description of various dynamical systems. In this exposition we are especially interested in applications which lead to proofs of periodic motions in various ... More

On the one-sided exit problem for fractional Brownian motionJan 26 2011We consider the one-sided exit problem for fractional Brownian motion (FBM), which is equivalent to the question of the distribution of the lower tail of the maximum of FBM on the unit interval. We improve the bounds given by Molchan (1999) and shed some ... More

Market depth and price dynamics: A noteMar 30 2004This note explores the consequences of nonlinear price impact functions on price dynamics within the chartist-fundamentalist framework. Price impact functions may be nonlinear with respect to trading volume. As indicated by recent empirical studies, a ... More

Computational Complexity Analysis of Multi-Objective Genetic ProgrammingMar 22 2012The computational complexity analysis of genetic programming (GP) has been started recently by analyzing simple (1+1) GP algorithms for the problems ORDER and MAJORITY. In this paper, we study how taking the complexity as an additional criteria influences ... More

Quantum theory of the real and the complexified projective lineSep 28 2005Quantum deformations of sets of points of the real and the complexified projective line are constructed. These deformations depend on the deformation parameter q and certain further parameters \lambda_{ij}. The deformations for which the subspace of polynomials ... More

A family of non-restricted $D=11$ geometric supersymmetriesJun 18 2014Sep 24 2015We construct a two parameter family of eleven-dimensional indecomposable Cahen-Wallach spaces with irreducible, non-flat, non-restricted geometric supersymmetry of fraction $\nu=\tfrac{3}{4}$. Its compactified moduli space can be parametrized by a compact ... More

The Torsion of Spinor Connections and Related StructuresNov 09 2006In this text we introduce the torsion of spinor connections. In terms of the torsion we give conditions on a spinor connection to produce Killing vector fields. We relate the Bianchi type identities for the torsion of spinor connections with Jacobi identities ... More

Grand Challenges in Planetary Nebulae Studies: Binary Evolution and MHDJun 23 2006We review work on the evolution of planetary nebulae and proto-planetaries via magneto-rotational mechanisms showing that a dynamo generated magnetic field can produce the energy and momentum needed to drive pPN and PNe outflows. Angular momentum considerations ... More

Where's the Disk?: LBV bubbles and Aspherical Fast WindsMay 02 1997Previous studies have explained the shapes of LBV nebulae, such as eta Car, by invoking the interaction of an isotropic fast wind with a previously deposited, slow aspherical wind (a "slow torus"). In this work I focus on the opposite scenario where an ... More

Physics Performance with the CMS Pixel DetectorDec 17 2014A large fraction of the results produced by the LHC experiments during the first run were made possible by precision vertexing detectors. The all-silicon tracking detector of the CMS experiment uses a pixel detector to do vertexing. This conference report ... More

First Alignment of the Complete CMS TrackerMar 12 2010This conference proceeding presents the first results of the full CMS Tracker alignment based on several million reconstructed tracks from the cosmic data taken during the commissioning runs with the detector in its final position and magnetic field present. ... More

Enlightenment, Knowledge, Ignorance, TemptationDec 14 2005Dec 17 2005I discuss the historical and conceptual roots of reasoning about the parameters of fundamental physics and cosmology based on selection effects. I argue concretely that such reasoning can and should be combined with arguments based on symmetry and dynamics; ... More

From "Not Wrong" to (Maybe) RightMar 24 2004This is a short, light spirited account of how some possibly important science actually happened. It very much conflicts with Popper's contention that the key to scientific progress is falsification.

Radical Conservatism and Nucleon DecayFeb 03 2000Feb 10 2000Unification of couplings, observation of neutrino masses in the expected range, and several other considerations confirm central implications of straightforward gauge unification based on SO(10) or a close relative and incorporating low-energy supersymmetry. ... More

Some Examples in the Realization of SymmetryOct 16 1997I briefly discuss three phenomena arising in recent work where the realization of symmetries in quantum mechanics is unusual. The first of these is, I believe, the very simplest realization of non-trivial confinement by a mechanism of charge-flux frustration. ... More

Asymptotic FreedomSep 11 1996I discuss how the basic phenomenon of asymptotic freedom in QCD can be understood in elementary physical terms. Similarly, I discuss how the long-predicted phenomenon of ``gluonization of the proton'' -- recently spectacularly confirmed at HERA -- is ... More

Superfluidity and Space-Time Translation Symmetry BreakingAug 27 2013I present a simple model that exhibits a temporal analogue of superconducting crystalline (LOFF) ordering. I sketch designs for minimally dissipative AC circuits, all based on time translation symmetry ($\tau$) invariant dynamics, exploiting weak links ... More

Introduction to {\it Quantum Matter}Sep 07 2011Nov 22 2011This paper records my opening remarks at Nobel Symposium 148, on Graphene and Quantum Matter, at Saltsj\"obaden, Sweden, in June 2010. After some broad comments on the quantum theory of matter as a frontier of physics, and some slightly more particular ... More

Anticipating a New Golden AgeAug 31 2007Oct 02 2007The standard model of fundamental interactions is remarkably successful, but it leaves an unfinished agenda. Several major questions seem ripe for exploration in the near future. I anticipate that the coming decade will be a Golden Age of discovery in ... More

Some Basic Aspects of Fractional Quantum NumbersJun 07 2002I review why and how physical states with fractional quantum numbers can occur, emphasizing basic mechanisms in simple contexts. The general mechanism of charge fractionalization is the passage from states created by local action of fields to states having ... More

Four Big Questions with Pretty Good AnswersJan 23 2002Feb 05 2002I discuss four big questions that can be importantly addressed using concepts from modern QCD. They concern the origin of mass, the feebleness of gravity, the uniqueness of physical laws, and the fate of matter when it is squeezed very hard.

The Future of Particle Physics as a Natural ScienceFeb 19 1997Feb 20 1997In the first part of the talk, I give a low-resolution overview of the current state of particle physics - the triumph of the Standard Model and its discontents. I review and re-endorse the remarkably direct and (to me) compelling argument that existing ... More

Beyond the Standard ModelApr 30 1993The standard model of particle physics is marvelously successful. However, it is obviously not a complete or final theory. I shall argue here that the structure of the standard model gives some quite concrete, compelling hints regarding what lies beyond. ... More

Detector Systems at CLICSep 15 2011The Compact Linear Collider CLIC is designed to deliver e+e- collisions at a center of mass energy of up to 3 TeV. The detector systems at this collider have to provide highly efficient tracking and excellent jet energy resolution and hermeticity for ... More

When teaching: Out with magnitudes, in with monochromatic luminosities!Jul 09 2008The goal of this document is to illustrate that teaching the concepts of magnitudes is a needless complication in introductory astronomy courses, and that use of monochromatic luminosities, rather than arbitrarily defined magnitudes, leads to a large ... More

X-rays from old star clustersJul 15 1999A brief overview is given of X-ray observations of old clusters. Most X-ray sources in old open clusters are interacting binaries, formed via evolution of a primordial binary, and emitting X-rays because of magnetic activity; however, a sizable fraction ... More

Observations of accretion disks in X-ray binariesSep 03 1998A brief overview is given of the observations of accretion disks in X-ray binaries, discussing their geometry, their effect on the rotation period of the accreting object, their optical and X-ray spectra, time variability, and radio emission and jets. ... More

Recent PHENIX Results on pi+, pi-, and eta Production in polarized pp Collisions at RHIC at sqrt(s) = 200 GeVAug 29 2008Measurements of double helicity asymmetries for inclusive hadron production in polarized proton-proton collisions are sensitive to spin-dependent parton distribution functions, in particular to the gluon distribution function. This study focuses on double ... More

Trace functions with applications in quantum physicsMay 08 2013Jul 02 2013We consider both known and not previously studied trace functions with applications in quantum physics. By using perspectives we obtain convexity statements for different notions of residual entropy, including the entropy gain of a quantum channel as ... More

Trace functions as Laplace transformsJul 01 2005Aug 02 2005We study trace functions on the form $ t\to\tr f(A+tB) $ where $ f $ is a real function defined on the positive half-line, and $ A $ and $ B $ are matrices such that $ A $ is positive definite and $ B $ is positive semi-definite. If $ f $ is non-negative ... More

Mechanical oscillations at the cellular scaleJun 21 2001Active phenomena which involve force generation and motion play a key role in a number of phenomena in living cells such as cell motility, muscle contraction and the active transport of material and organelles. Here we discuss mechanical oscillations ... More

Comparative Study of $Z'$ Searches in $e^+e^-$ and $e^-e^-$ ScatteringFeb 29 1996We consider indirect searches for additional neutral vector bosons in $e^+e^-$ and $e^-e^-$ collisions, and compare these two linear collider modes with similar analysis procedures and assumptions. Discovery limits and resolving power are discussed in ... More

Slepton Production in Polarized $γγ$ ScatteringSep 27 1995We study slepton pair-production in polarized $\gamma\gamma$ scattering. It turns out that the combined use of polarization and angular correlations greatly enhances the resolving power of this reaction.

Accelerating QDP++/Chroma on GPUsNov 23 2011Extensions to the C++ implementation of the QCD Data Parallel Interface are provided enabling acceleration of expression evaluation on NVIDIA GPUs. Single expressions are off-loaded to the device memory and execution domain leveraging the Portable Expression ... More

Noncommutative Spaces and GravityOct 21 2005This is an introduction to an algebraic construction of a gravity theory on noncommutative spaces which is based on a deformed algebra of (infinitesimal) diffeomorphisms. We start with some fundamental ideas and concepts of noncommutative spaces. Then ... More

Uncertain for A Century: Quantum Mechanics and The Dilemma of InterpretationFeb 07 2016Quantum Mechanics, the physical theory describing the microworld, represents one of science's greatest triumphs. It lies at the root of all modern digital technologies and offers unparalleled correspondence between prediction and experiments. Remarkably, ... More

General isotropic flags are general (for Grassmannian Schubert calculus)Jan 17 2008Jul 21 2008We show that general isotropic flags for odd-orthogonal and symplectic groups are general for Schubert calculus on the classical Grassmannian in that Schubert cells defined by such flags meet transversally. This strengthens a result of Belkale and Kumar ... More

Enumerative geometry for real varietiesSep 12 1996We discuss the problem of whether a given problem in enumerative geometry can have all of its solutions be real. In particular, we describe an approach to problems of this type, and show how this can be used to show some enumerative problems involving ... More

Lepton Flavor Violation at the LHCOct 12 2007In supersymmetric scenarios, the seesaw mechanism involving heavy right-handed neutrinos implies sizable lepton flavor violation (LFV) in the slepton sector. We discuss the potential of detecting LFV processes at the LHC in mSUGRA+seesaw scenarios and ... More

The chemistry induced by mechanical loadMay 11 2016Results in the field of mechanochemistry are summarized. For example under mechanical load often a solvolysis is observed instead of a simple homolytic bond rupture. Also a mechanically induced redox reaction was reported experimentally and could be modelled ... More

Noncommutative complex analytic spacesJun 07 2006In this paper, we define NC complex spaces as complex spaces together with a structure sheaf of associative algebras in such a way that the abelization of the structure sheaf is the sheaf of holomorphic functions.

Groups in simple theoriesApr 25 1997Groups definable in simple theories retain the chain conditions and decomposition properties known from stable groups, up to commensurability. In the small case, if a generic type of G is not foreign to some type q, there is a q-internal quotient. In ... More

Semidefinite programming bounds for error-correcting codesFeb 04 2019This chapter is written for the forthcoming book "A Concise Encyclopedia of Coding Theory" (CRC press), edited by W. Cary Huffman, Jon-Lark Kim, and Patrick Sol\'e. This book will collect short but foundational articles, emphasizing definitions, examples, ... More

Problems on homology manifoldsOct 17 2003Mar 18 2009A list of problems prepared for the proceedings of the Workshop on Exotic Homology Manifolds, Oberwolfach June 29-July 5 2003.

Coherent Control of Floquet-Mode Dressed Plasmon PolaritonsJun 07 2012Sep 15 2015We study the coherent properties of plasmon polaritons optically excited on periodic nanostructures. The gold grains are coupled to a single mode photonic waveguide which exhibits a dramatically reduced transmission originating from the derived quantum ... More

Quantum Criticality and Population Trapping of Fermions by Non-Equilibrium Lattice ModulationsSep 18 2011Mar 04 2016An ultracold gas of interacting fermionic atoms in a three-dimensional optical lattice is considered, where the lattice potential strength is periodically modulated. This non-equilibrium system is non-perturbatively described by means of a Keldysh-Floquet-Green's ... More

Composition of operator ideals and their regular hullsApr 24 1996Given two quasi-Banach ideals \oid{A}{}{} and \oid{B}{}{} we investigate the regular hull of their composition - $(\oid{A}{}{} \circ \oid{B}{}{})^{reg}$. In concrete situations this regular hull appears more often than the composition itself. As a first ... More

Hilbert H*-modules and Hilbert modules over (non-self-adjoint) operator algebras -- a reference overview IIMay 07 1996The two reference lists contain 54/22 references of papers and preprints concerned with the theory and/or various applications of Hilbert modules over Hilbert $*$-algebras and over (non-self-adjoint) operator algebras. They are far from being complete, ... More

Pieri-type formulas for maximal isotropic Grassmannians via triple intersectionsAug 29 1997We give an elementary proof of the Pieri-type formula in the cohomology of a Grassmannian of maximal isotropic subspaces of an odd orthogonal or symplectic vector space. This proof proceeds by explicitly computing a triple intersection of Schubert varieties. ... More

Explicit Enumerative Geometry for the Real Grassmannian of Lines in Projective SpaceOct 31 1995We extend the classical Schubert calculus of enumerative geometry for the Grassmann variety of lines in projective space from the complex realm to the real. Specifically, given any collection of Schubert conditions on lines in projective space which generically ... More

An analysis of the Rüschendorf transform - with a view towards Sklar's TheoremDec 17 2013Jul 08 2015In many applications including financial risk measurement, copulas have shown to be a powerful building block to reflect multivariate dependence between several random variables including the mapping of tail dependencies. A famous key result in this field ... More

Some real and unreal enumerative geometry for flag manifoldsFeb 24 2000Jul 19 2000We present a general method for constructing real solutions to some problems in enumerative geometry which gives lower bounds on the maximum number of real solutions. We apply this method to show that two new classes of enumerative geometric problems ... More

The special Schubert calculus is realApr 27 1999We show that the Schubert calculus of enumerative geometry is real, for special Schubert conditions. That is, for any such enumerative problem, there exist real conditions for which all the a priori complex solutions are real.

Exceptional holonomy and Einstein metrics constructed from Aloff-Wallach spacesApr 27 2010We investigate cohomogeneity-one metrics whose principal orbit is an Aloff-Wallach space SU(3)/U(1). In particular, we are interested in metrics whose holonomy is contained in Spin(7). Complete metrics of this kind which are not product metrics have exactly ... More

Real Schubert Calculus: Polynomial systems and a conjecture of Shapiro and ShapiroApr 24 1999Boris Shapiro and Michael Shapiro have a conjecture concerning the Schubert calculus and real enumerative geometry and which would give infinitely many families of zero-dimensional systems of real polynomials (including families of overdetermined systems)--all ... More

Characters and Brauer trees of the covering group of $^2E_6(2)$Sep 08 2016Let $G$ be the finite simple Chevalley group of type $^2E_6(2)$. It has a Schur multiplier of type $C_2^2 \times C_3$. We determine the ordinary character tables of the central extensions $3.G$, $6.G$, $(2^2\times 3).G$ of $G$ and their extensions by ... More

Natural TopologyOct 23 2012We give a theoretical and applicable framework for dealing with real-world phenomena. Joining pointwise and pointfree notions in BISH, natural topology gives a faithful idea of important concepts and results in intuitionism. Natural topology is well-suited ... More

Mod p representations on elliptic curvesJun 11 2004Modular Galois representations into GL_2(F_p) with cyclotomic determinant arise from elliptic curves for p = 2,3,5. We show (by constructing explicit examples) that such elliptic curves cannot be chosen to have conductor as small as possible at all primes ... More

Distortion in Groups of Circle and Surface DiffeomorphismsMay 28 2007In these lectures we consider how algebraic properties of discrete subgroups of Lie groups restrict the possible actions of those groups on surfaces. The results show a strong parallel between the possible actions of such a group on the circle $S^1$ and ... More

Markov chain Monte Carlo importance samplers for Bayesian models with intractable likelihoodsApr 11 2019We consider the efficient use of an approximation within Markov chain Monte Carlo (MCMC), with subsequent importance sampling (IS) correction of the Markov chain inexact output, leading to asymptotically exact inference. We detail convergence and central ... More

Exact computation over topological spacesJun 02 2018We give an exposition of Natural Topology (NToP), which highlights its advantages for exact computation. The NToP-definition of the real numbers (and continuous real functions) matches recent expert recommendations for exact real computation (see [Bauer&Kavkler2008] ... More

Toric ideals, real toric varieties, and the algebraic moment mapDec 03 2002Apr 18 2008This is a tutorial on some aspects of toric varieties related to their potential use in geometric modeling. We discuss projective toric varieties and their ideals, as well as real toric varieties and the algebraic moment map. In particular, we explain ... More

Notes on Chain Recurrence and Lyapunonv FunctionsApr 24 2017This short expository note provides an introduction to the concept of chain recurrence in topological dynamics and a proof of the existence complete Lyapunov functions for homeomorphisms of compact metric spaces due to Charles Conley. I have used it as ... More

Hochschild Cohomology for Complex Spaces and Noetherian SchemesMar 03 2003The classical HKR-theorem gives an isomorphism of the n-th Hochschild cohomology of a smooth algebra and the n-th exterior power of its module of K\"ahler differentials. Here we generalize it for simplicial, graded and anticommutative objects in ``good ... More

Relations between the ranks and cranks of partitionsAug 06 2002New identities and congruences involving the ranks and cranks of partitions are proved. The proof depends on a new partial differential equation connecting their generating functions.

Dimensional groups and fieldsNov 30 2015Sep 19 2018We shall define a general notion of dimension, and study groups and rings whose interpretable sets carry such a dimensio. In particular, we deduce chain conditions for groups, definability results for fields and domains, and show that pseudofinite groups ... More

On Hahn-Banach type theorems for Hilbert C*-modulesSep 30 1996Feb 14 2000We show three Hahn-Banach type extension criteria for (sets of) bounded C*-linear maps of Hilbert C*-modules to the underlying C*-algebras of coefficients. One criterion establishes an alternative description of the property of (AW*-) C*-algebras to be ... More

Towards an Account of Extraposition in HPSGFeb 21 1995This paper investigates the syntax of extraposition in the HPSG framework. We present English and German data (partly taken from corpora), and provide an analysis using lexical rules and a nonlocal dependency. The condition for binding this dependency ... More

Rotation Numbers for $S^2$ diffeomorphismsDec 28 2014These largely expository notes describe the properties of the function ${\cal R}$ which assigns a number to a $4$-tuple of distinct fixed points of an orientation preserving homeomorphism or diffeomorphism of $S^2$.

Correlation effects on the doped triangular lattice in view of the physics of sodium-rich Na$_x$CoO$_2$Jul 24 2008Jan 30 2009The peculiar correlation effects on the triangular lattice are studied by means of the rotationally invariant slave boson method in a cellular cluster approach. Hence nonlocal correlations are included in a short-range regime. Their impact for the single-band ... More

A controlled-topology proof of the product structure theoremOct 03 2006The controlled end and h-cobrodism theorems (Ends of maps I, 1979) are used to give quick proofs of the Top/PL and PL/DIFF product structure theorems.